Largely because of riding in cars, you are used to horizontal circular motion. Vertical circular motion would be a novelty. In this sample problem, such motion seems to defy the gravitational force.
In a 1901 circus performance, Allo Dare Devil Diavolo introduced the stunt of riding a bicycle in a loop the loop. Assuming that the loop is a circle with radius R=2.7m, what is the least speed v that Diavolo and hisbicycle could have at the top of the loop to remain in contact with it there?

Explanation

To solve the problem of finding the least speed \( v \) that Diavolo and his bicycle could have at the top of the loop to remain in contact with it, we can follow these steps:

### Step 1: Understand the Forces at the Top of the Loop
At the top of the loop, two forces act on Diavolo:
1. The gravitational force \( mg \) acting downward.
2. The normal force \( N \) also acting downward (since the bicycle must stay in contact with the loop).

For Diavolo to remain in contact with the loop, the centripetal force required for circular motion must be provided by the sum of these two forces.
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